Quality Engineering

answer question (e) (f) (g) only thanks

4. The data set refers to the ball shear strengths (X) of a product at a bonding temperature of 240C: Mon 1 2 3 4 Tue SI SI S2 S2 SI SI S2 S2 SI SI S2 S2 SI SI S2 S2 SI SI 87.5 80.1 77.6 75.8 88.7 74.8 83.7 79.8 88.8 76.9 Wed 86.5 68.0 84.0 75.7 56.4 62.9 71.9 66.2 63.1 73.7 60.8 51.6 69.9 52.6 74.5 63.4 68.5 67.0 77.5 71.8 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 82.6 73.1 84.2 60.0 67.8 67.6 70.1 77.6 54.5 74.6 59.4 78.4 57.3 71.4 74.9 70.6 59.0 65.3 62.5 79.0 75.6 66.3 67.5 68.1 69.2 62.7 61.1 58.9 56.3 58.3 65.5 65.5 71.4 54.1 69.4 63.8 66.5 67.1 84.2 66.4 69.2 76.4 64.0 74.6 69.2 85.7 66.9 83.4 76.9 64.1 80.1 73.3 75.3 82.1 Thu 69.4 87.5 68.1 65.4 63.8 58.4 70.1 52.0 75.6 70.1 67.6 60.0 64.0 55.1 74.8 60.7 65.5 62.8 61.8 69.5 70.0 59.2 69.3 80.6 Fri Sat 73.7 74.2 63.6 S2 S2 SI SI S2 S2 73.5 73.5 67.1 71.5 63.1 54.0 78.1 57.3 87.0 (a) Taking all the 120 observations together, find Xmin, Xmax, R, and the mean and standard deviation Answers: 51.6, 88.8, 37.2, 69.72, 8.90. (b) Plot the histogram for X. How does a change in the number of intervals affect the plot? Plot the normal probability plot (NPP). (c) Given that LSL = 40, compute the fraction non-conforming (FNC). (d) Plot the X and R charts. Apply the synthesizing rules. Is the process in control? (e) Based on the 24 X's in (d), plot the histogram and the NPP. Compare the distributions of X and X. Find the mean and standard deviation of X (f) From the data/results in (a), (d) and (e), show empirically whether the following relationships hold: 0170x/tn 0, z/d2 What is the practical significance of the relationships in SPC? (g) Assume that the process mean shifts to 78. For the X chart in (d), what is the probability of not detecting the shift in the first sample plotted after the shift? Use only synthesizing rule 1